Electron. J. Diff. Eqns., Vol. 2000(2000), No. 10, pp. 119.
A second eigenvalue bound for the Dirichlet Schrodinger equation
wtih a radially symmetric potential
Craig Haile
Abstract:
We study the timeindependent Schrodinger
equation with radially symmetric potential
,
,
on a bounded domain
in
,
with Dirichlet boundary conditions.
In particular, we compare the eigenvalue
of
the operator
on
with the eigenvalue
of the same operator
on a ball ,
where
has radius such
that the first eigenvalues are the same,
.
The main result is to show
.
We also give an extension of the main
result to the case of a more general elliptic eigenvalue problem
on a bounded domain with Dirichlet boundary conditions.
Submitted August 24, 1999. Published Janaury 28, 2000.
Math Subject Classifications: 35J10, 35J15, 35J25, 35P15.
Key Words: Schrodinger eigenvalue equation, Dirichlet boundary conditions,
eigenvalue bounds, radially symmetric potential.
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Craig Haile
Department of Mathematics and Physics
College of the Ozarks
Point Lookout, MO 657260017, USA
email: haile@cofo.edu 
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